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Cooperation in Large Societies


  • Francesc Dilmé

    () (Department of Economics, University of Pennsylvania)


Consider the following situation involving two agents who belong to a large society. One of the agents needs help to avoid a big loss. The other agent may either incur a low cost to help him or do nothing. If agents do not recognize each other, providing incentives for socially optimal behavior (helping) is, in general, very difficult. We use a repeated anonymous random matching setting in a large society to understand how, in the previous situation, help may take place in equilibrium. We find explicit equilibria that, unlike other models proposed in the literature, feature smooth aggregate behavior over time and robustness to many perturbations, such as the presence of behavioral types or trembles. We consider the joint limit of increasing the size of the society and making it more interactive (or patient.) Under this limit, our equilibria resemble the tit-for-tat strategy for the prisoner’s dilemma, introducing some small probability of forgiveness. The model is also applied to bilateral trade, where the mechanism used to spread deviations is transmissive instead of contagious. The smooth evolution of the aggregate variables over time makes the model suitable for empirical work.

Suggested Citation

  • Francesc Dilmé, 2012. "Cooperation in Large Societies," PIER Working Paper Archive 12-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:12-011

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    References listed on IDEAS

    1. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    2. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
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    More about this item


    Cooperation; Many Agents; Repeated Game; Unilateral Help;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers

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